Possibilistic Defeasible Logic Programming (\Pdelp) is a logic programming language which combines features from argumentation theory and logic programming, incorporating the treatment of possibilistic uncertainty at object-language level. This paper presents a first approach towards extending \Pdelp to incorporate fuzzy constants and fuzzy propositional variables. We focus on how to characterize the resulting, extended language, and how to deal with conflicting arguments in the context of the proposed framework.